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Deciphering the Dynamical Echoes of Dwarf Galaxies on Galactic Disks Sukanya Chakrabarti (RIT) Collaborators: Frank Bigiel (Heidelberg) Leo Blitz (UCB), Philip Chang (UWM), Victor Debattista (UCLan), Alice Quillen (U.Rochester), Roberto Saito (PUC, Chile), Evan Kirby (Caltech)

Tuesday, July 8, 14 Overview • Cold gas as tracer of perturbing dark-matter dominated dwarf galaxies

• Galaxies with optical companions : Proof of Principle

Tuesday, July 8, 14 Overview • Cold gas as tracer of perturbing dark-matter dominated dwarf galaxies

• Galaxies with optical companions : Proof of Principle

Tuesday, July 8, 14 Overview • Cold gas as tracer of perturbing dark-matter dominated dwarf galaxies

• Galaxies with optical companions : Proof of Principle

Tuesday, July 8, 14 Overview • Cold gas as tracer of perturbing dark-matter dominated dwarf galaxies

• Galaxies with optical companions : Proof of Principle

Tuesday, July 8, 14 Overview • Cold gas as tracer of perturbing dark-matter dominated dwarf galaxies

• Galaxies with optical companions : Proof of Principle • The Milky Way

Tuesday, July 8, 14 Analogy with Planetary Dynamics: Discovery of Neptune

• Urbain Le Verrier: Aug 13 1846: predicted azimuth of Neptune

Tuesday, July 8, 14 Analogy with Planetary Dynamics: Discovery of Neptune

• Urbain Le Verrier: Aug 13 1846: predicted azimuth of Neptune

Tuesday, July 8, 14 Extended HI disks as tracer of sub-halo interactions

• cosmological simulations predict most sub-halos of a given mass are in the outer parts of the halo • M83’s HI disk reaches to ~ 100 kpc -- where simulations expect the sub-structure to be Springel et al. 2008

Tuesday, July 8, 14 Tidal Imprints of dark-matter dominated dwarf galaxies on outskirts of spirals

• Coldest Component Responds the Most! Atomic hydrogen Extended HI disks reach to • (HI) Maps several times the optical radius -- largest cross- section for interaction • Gas has short-term memory. Footprints of Dark • The best of Sub-Halos hydrodynamics!

Tuesday, July 8, 14 Disturbances in HI disks in Local Spirals: Proof of Principle

Tuesday, July 8, 14 M51

HI Map optical image

-imϕ am(r)=∫Σ(r,ϕ)e dϕ Local Fourier Amplitudes of HI data: Metric of Comparison to simulations

Tuesday, July 8, 14 M51

HI Map optical image

-imϕ am(r)=∫Σ(r,ϕ)e dϕ Local Fourier Amplitudes of HI data: Metric of Comparison to simulations

Tuesday, July 8, 14 M51

HI Map optical image

-imϕ am(r)=∫Σ(r,ϕ)e dϕ Local Fourier Amplitudes of HI data: Metric of Comparison to simulations

Tuesday, July 8, 14 M51 : Proof of Principle

Chakrabarti, Bigiel, Chang & Blitz, 2011

Tuesday, July 8, 14 Variance Vs Variance

Best-ﬁts -- close to origin on variance vs variance plot (S1-S1-4), shown at best-ﬁt time. “Variants” include varying initial conditions (ICs), interstellar medium (ISM), star formation prescription, orbital inclination, etc. Our estimate of Ms (1:3) close to observational numbers. Tuesday, July 8, 14 Variance Vs Variance

• ~1:100 satellite, Rperi = 7kpc (close agreement with Koribalski & Sanchez 09) (global fourier amplitudes) • Method works for 1:3 - 1:100 mass ratio satellites

Tuesday, July 8, 14 Galaxies with known optical companions contd.

• ~1:100 satellite, Rperi = 7kpc (close agreement with Koribalski & Sanchez 09) (global fourier amplitudes) • Method works for 1:3 - 1:100 mass ratio satellites

Tuesday, July 8, 14 HI Map of Milky Way HI maps: Levine, Blitz & Heiles 2006. What caused these structures well outside the solar circle? -imϕ am(r)=∫Σ(r,ϕ)e dϕ

Tuesday, July 8, 14 Ms Rperi inclination Simulations

fgas 1:10-1:1000 0.1-50kpc (0.1-0.3), EQS (isothermal-

Parameter space survey of simulations to explain observed disturbances in HI map of Milky Way. Chakrabarti & Blitz 2009, Chakrabarti & Blitz 2011.

Tuesday, July 8, 14 Initial Conditions, Orbits -- what really matters?

• Not very sensitive to initial conditions (for parameters comparable to spirals). CB09 -- Ms and Rperi are what really matter. Quillen et al. 2009 -- radial mixing of stellar metallicities caused by satellite of comparable mass and pericenter distance

Tuesday, July 8, 14 The classical Milky Way Satellites: from Orbits to Tides • Integrate backwards the equation of motion for known Milky Way satellites including dynamical friction in orbit integrator test particle code. ¨r = ∂/∂r ϕMW + FDF/Msat • Observational constraints: HST proper motions + Sgr tidal stream stream. Take HST proper motion The Tidal Players: LMC, Sgr, uncertainties into account CB09’s putative satellite by randomly sampling the Chakrabarti et al., 2014b distribution

Tuesday, July 8, 14 but how can we get masses of tidally disrupting satellites??

• the Sgr dwarf galaxy is ... the closest, most massive known Milky Way satellite. To study the tidal effect of the known satellites on the Milky Way disk, we need to ﬁgure out a way to get the progenitor mass of Sgr!

Tuesday, July 8, 14 An Eccentricity-Mass Relation for Galaxies

Tuesday, July 8, 14 An Eccentricity-Mass Relation for Galaxies •Satellite at pericenter, know its X,V. Assume ϕ(r), with normalization (total mass, MT) undetermined. Relate MT to orbital eccentricity, e. e = (Ra-Rp)/(Ra+Rp) 2 2 • E = 1/2 vr + 1/2 vt + ϕ(r), L = vtr, E = 2 2 2 1/2 vr + L /2r + ϕ(r)

•Assume Hernquist form for potential: E = 2 + 2 2 1/2 vr L /2r - GMT/(r+a)

•Given X,V, assumed ϕ(r): in the absence of dynamical friction: unique relation between e and MT. (Chakrabarti et al. 2014a, arXiv: 1401.4182)

Tuesday, July 8, 14 • Given a satellite’s current X and V, its past orbit depends on the MW mass and on its mass thru dynamical friction and tides • Average eccentricity of orbit in GADGET simulations agrees closely with orbit integration calculations, which we can use to sample the parameter space

Tuesday, July 8, 14 • The maximum excursion of a satellite’s orbit (when you include dynamical friction) gives you a measure of its progenitor mass. Can explain the Belokurov et al. 2014 data. • Main uncertainty in Sgr progenitor mass due to the fact that observational uncertainties in apocenters have not been quantiﬁed! • Deeper observations (GAIA) should improve constraints on Sgr mass

Tuesday, July 8, 14 9 10 • Sgr masses less than 10 Msun and greater than 5x10 Msun 12 ruled out for likely MW masses ~ 1 - 2.5 x 10 Msun. • This is a robust and efﬁcient method to estimate masses of tidally disrupting satellites (Chakrabarti et al. 2014a).

Tuesday, July 8, 14 From Orbits to Tides

Test particle calculations to survey the parameter space and follow up interesting regions with full SPH simulations (Chakrabarti et al. 2014b)

Tuesday, July 8, 14 The Tidal Players of the Milky Way

Purcell et al. (+Chakrabarti) 2011 Previous work has focused on single satellites and/or N- body only with ad- hoc initial conditions

Tuesday, July 8, 14 Are the known satellites enough?

known satellites alone do not match the planar disturbances

Tuesday, July 8, 14 Are the known satellites enough?

known satellites alone do not match the planar disturbances

Tuesday, July 8, 14 Are the known satellites enough?

known satellites alone do But -- Sgr does produce a not match the planar warp that’s pretty close to disturbances the data

Tuesday, July 8, 14 Summary & Future • Analysis of perturbations in cold gas on outskirts of galaxies: constrains mass,R,and azimuth of dark (or luminous) perturbers. New method to characterize satellites (to see dark galaxies). Method tested for satellites with mass ratio: ~1:100 - 1:3. Extended to infer dark matter density proﬁle of spirals. • Using robust initial conditions (simulations can’t be used to make accurate predictions unless they start correctly!) and reliable mass estimates, we ﬁnd that the classical MW satellites can’t explain observed disturbances.

Search for putative satellite in VISTA data

Tuesday, July 8, 14